There will no longer be fear or hurt between man and animals. Isa. 11:6-9 - "The wolf shall dwell with the lamb; and the leopard shall lie down with the kid; and the calf and the young lion and the fatling together; and a little child shall lead them. And the cow and the bear shall feed; their young ones shall lie down together; and the lion shall eat straw like the ox. And the suckling child shall play on the hole of the asp, and the weaned child shall put his hand on the cockatrice den. They shall not hurt nor destroy in all my holy mountain: for the earth shall be full of the knowledge of the Lord,as the waters cover the sea."

Christ will rule with the rod of iron and Israel will be head of all nations. Once again, Isa. 2:1-4 - "The word that Isaiah, the son of Amoz saw concerning Judah and Jerusalem. And it shall come to pass in the last days, that the mountain of the Lord's house shall be established in the top of the mountain of the Lord, to the house of the God of Jacob; and he will teach us of his ways, and we will walk in his paths, for out of Zion shall go forth the law, and the Word of the Lord from Jerusalem. And He shall judge among the nations, and shall rebuke many people; and they shall beat their swords into plowshares, and their spears into pruning hooks; nation shall not lift up the sword against nation, neither shall they learn war any more."

During the 1,000 year millennium period, Satan is bound in the bottomless pit. 

Rev. 20:1-7 - "And I saw an angel come down from Heaven, having the key of the bottomless pit and a great chain in his hand. And he laid hold on the dragon, the old serpent, which is the Devil, and Satan, and bound him a thousand years. And cast him into the bottomless pit, and shut him up, and set a seal upon him, that he should deceive the nations no more. till the thousand years should be fulfilled, and after that he must be loosed a little season. And I saw thrones and they sat upon them, and judgment was given unto them, and I saw the souls of them that were beheaded for the witness of Jesus, and for the Word of God, and which had not worshiped the beast, neither his image, neither had received his mark upon their foreheads, or in their hands; and they lived and reigned with Christ a thousand years."

"But the rest of the dead lived not again until the thousand years were finished. This is the first resurrection. Blessed and holy is he that hath part in the first resurrection: on such the second death hath no power, but they shall be priests of God, and of Christ, and shall reign with him a thousand years. And when the thousand years are expired, Satan shall be loosed out his prison."

The beast and the false prophet have already been cast into the lake of fire. Rev. 19:20 - "And the beast was taken, and with him the false prophet that wrought miracles before him, with which he deceived them that had received the mark of the beast, and them that worshiped his image. These both were cast alive into a lake of fire with brimstone."

After the millennium - God, one final time, shows the character and nature of Satan. Satan is loosed from the bottomless pit for a short time. Rev. 20:7 - "And when the thousand years are expired, Satan shall be loosed out of his prison."